Discrete Mathematics with Ducks

Preface for Instructors and Other Teachers

Preface for Students and Other Learners

Theme: The Basics

1 Counting and Proofs

2 Sets and Logic

3 Graphics and Functions

4 Induction

5 Algorithms with Ciphers

Theme I Supplement

6 Binomial Coefficients and Pascal's Triangle

7 Balls and Boxes and PIE: Counting Techniques

8 Recurrences

9 Cutting Up Food: Counting and Geometry

III Theme: Graph Theory

10 Trees

11 Euler's Formula and Applications

12 Graph Traversals

13 Graph Coloring

Theme III Supplement: Problems on the Theme of Graph Theory

IV Other Material

14 Probability and Expectation

15 Fun with Cardinality

16 Number Theory

17 Computational Complexity

A Solutions to Check Yourself Problems

B Solutions to Bonus Check-Yourself Problems

C The Greek Alphabet and Some Uses for Some Letters

D List of Symbols

Bibliography

Index

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• Teoria combinatória e dos grafos
• A matemática discreta

Chromatic Number;Mod 12;Sets and Logic;Bubble Sort Algorithm;Algorithms with Ciphers;Euler Circuit;Graph Traversals;Fibonacci Number;Binomial Coefficients and Pascal's Triangle;Combinatorial Proof;Balls and Boxes and PIE-Counting Techniques;Pigeonhole Principle;Hamilton Circuit;Petersen Graph;Degree Sequence;Binomial Coefficients;Fibonacci;Computer Algebra System;Duck;Pascal's Triangle;White Duck;Inductive Hypothesis;Bipartite Graph;Planar Graph;Chromatic Index;Modular Arithmetic;Kth Differences;Binary Decision Tree;Kruskal's Algorithm;Nonplanar Graph